Quasi-Wilson nonconforming element approximation for nonlinear dual phase lagging heat conduction equations

Accuracy analysis of quasi-Wilson nonconforming element for nonlinear dual phase lagging heat conduction equations is discussed and higher order error estimates are derived under semi-discrete and fully-discrete schemes. Since the nonconforming part of quasi-Wilson element is orthogonal to biquadratic polynomials in a certain sense, it can be proved that the compatibility error of this element is of order O(h^2)/O(h^3) when the exact solution belongs to H^3(@W)/H^4(@W), which is one/two order higher than its interpolation error. Based on the above results, the superclose properties in L^2-norm and broken H^1-norm are deduced by using high accuracy analysis of bilinear finite element. Moreover, the global superconvergence in broken H^1-norm is derived by interpolation postprocessing technique. And then, the extrapolation result with order O(h^3) in broken H^1-norm is obtained by constructing a new extrapolation scheme properly, which is two order higher than the usual error estimate. Finally, optimal order error estimates are deduced for a proposed fully-discrete approximate scheme.

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